CAIE IGCSE Mathematics Extended E1.12 Rates Questions

Practise density, fuel use, flow and planting rates alongside average-speed problems, with conversions between compound units and time forms.

Exam points

apply density, planting, fuel or flow rates after converting area, volume, mass and time units
calculate an overall consumption rate from combined totals rather than averaging section rates
use total distance divided by total time for average speed and state the requested compound unit

Covered syllabus points

E1.12.1 Use common measures of rate.E1.12.2 Apply other measures of rate.E1.12.3 Solve problems involving average speed

[Maximum number: 4]

NOT TO SCALE

The diagram shows a field, ABCD with B north of A.
BD is a path across the field.
$A B=85 \mathrm{~m}, A D=72 \mathrm{~m}, B D=129 \mathrm{~m}$ , angle $B D C=39^{\circ}$ and angle $B C D=60^{\circ}$ .

Trees are planted in the field.

The number of trees planted is 1100 per hectare.
Calculate the total number of trees planted in the field. [ 1 hectare $=10000 \mathrm{~m}^{2}$ ]
The length of the rectangle is 80 cm , correct to the nearest 10 cm .

Calculate the upper bound of the width of the rectangle. cm

972 or 973
M1 for $[\triangle ABD]\frac{1}{2}\times85\times129\sin31.6^\circ$ oe
or $\frac{1}{2}\times129\times\text{their }44.5$ oe
M1 for $[\triangle BCD]\frac{1}{2}\times129\times\text{their }147\times\sin39^\circ$ oe
M1 for $\frac{\text{their total area}}{10000}\times1100$

[Maximum number: 2]

Darpan runs a distance of 12 km and then cycles a distance of 26 km .
His running speed is $x \mathrm{~km} / \mathrm{h}$ and his cycling speed is $10 \mathrm{~km} / \mathrm{h}$ faster than his running speed. He takes a total time of 2 hours 48 minutes.

Calculate the number of minutes Darpan takes to run the 12 km .

84 to 84.01...
FT $\frac{720}{\text{their positive answer}}$ to 3 sf or better
M1 for $\frac{12}{\text{their positive answer}}\times60$ oe

[Maximum number: 3]

(a)

Kaito runs along a 12 km path at an average speed of $x \mathrm{~km} / \mathrm{h}$ .

[ 3 ]

(i)

Write down an expression, in terms of x, for the number of hours he takes.
hours [1]

[ 1 ]

$\frac{12}{x}$ or $12\div x$ final answer

(ii)

Find the number of hours it takes Yuki to walk along the 12 km path.
hours

[ 2 ]

3
M1 for $\frac{12}{\text{their }8-4}$ or $\frac{12}{\text{their }8}+1.5$ oe or for answer $\frac{12}{\text{their }8}$

All question bank results loaded

Covered syllabus points

Question 1

Question 2

Question 3

Question (a)

Question (i)

Question (ii)